American Institute of Aeronautics and Astronautics 092407

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Development of a Fast RANS Based

Noise Estimation Method for High Lift Systems

Michael Pott-Pollenske1, Jochen Wild,

2 and Jan Delfs

3

Deutsches Zentrum für Luft- und Raumfahrt, Braunschweig, 38108, Germany

A meaningful reduction of high lift systems noise generation can only be achieved by

means of a combined aerodynamic and aeroacoustic optimization process. The DLR project

LEISA combines and focuses activities in the research areas of high lift system design, flow

control and aeroacoustic design methods. The development of a noise estimation tool that

enables the assessment of high lift devices noise generation during the design process is one

substantial part of the LEISA project. Based on the use of turbulence and flow field data

provided by RANS based flow solvers a very fast noise assessment method was developed

and experimentally validated allowing a comparison of different aerodynamic

configurations. In order to test and validate this approach, numerical and experimental

studies on trailing edge noise were conducted using a NACA0012 2D airfoil. The scope of

these tests was to generate different turbulence levels at the airfoil’s trailing edge and to

examine on the one hand the noise generation and on the other hand the experimentally and

numerically derived mean and fluctuating velocities at the trailing edge. The comparison of

the computed turbulence data with measured data revealed a good agreement between

measured and computed data which were consequently regarded adequate to serve as input

for the acoustic design tool. The noise prediction performed for the NACA0012 test case

showed a systematic trend to higher sound pressure levels for higher turbulence levels at the

trailing edge as was also observed in the measurement results. This in fact indicated the

principle ability of this method to distinguish between the noise generation of different

aerodynamic configurations. One basic approach within the project LEISA was the design of

a low noise 3 element high lift system. Assuming the trailing edge noise mechanism to be

relevant for slat noise generation this prediction method consequently was applied to these

test cases as well and revealed a noise reduction of about 4 dB for the new high lift system

which compares well to the measured noise reduction of about 5 dB. Therefore this method

may serve as an engineering tool within the aerodynamic optimization process of high lift

systems.

Nomenclature

a0 = speed of sound

b = span width

k = wave number

kt = turbulence kinetic energy

L = mean turbulence length scale

Ma = Mach number

p’ = sound pressure

r = radius

r0 = distance to trailing edge

R = observer distance to trailing edge

Sr = Strouhal number

u’ = local fluctuating velocity

1 Research Scientist, Inst. of Aerodynamics and Flow Technology, michael.pott-pollenske@dlr.de, AIAA member.

2 Research Scientist, Inst. of Aerodynamics and Flow Technology, jochen.wild@dlr.de, AIAA member.

3 Head of Technical Acoustics Dept., Inst. of Aerodynamics and Flow Technology, jan.delfs@dlr.de, AIAA

member.

15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)11 - 13 May 2009, Miami, Florida

AIAA 2009-3312

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

American Institute of Aeronautics and Astronautics 092407

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U = mean local flow velocity

U’rms = rms-value of velocity fluctuations’

V0 = integration volume

υr = flow velocity component in radial direction

υθ = flow velocity component in azimuthal direction

z0 = spanwise extend of the trailing edge

α = angle of attack

λ = wavelength

ϕ = polar angle between observer position and trailing edge

ρ = fluid density

θ = azimuth of observer position to trailing edge

θ0 = azimuth to trailing edge

ω = angular frequency

ωt = turbulence dissipation rate

I. Introduction

oise impact in the vicinity of large airports due to arriving and departing aircraft represents a problem of

increasing importance. As a consequence, the development of future airliners will have to provide solutions to

this problem. Basically two ways of reducing the noise impact are conceivable:

• Reduction of the acoustic intensity of the noise source or

• Increasing the distance of the noise source from the exposed region.

The first approach addresses the aeroacoustic design of the aircraft and of its components, the second one involves

the aerodynamic performance of the aircraft. It is obvious, that if means for source noise reductions degrade the

aerodynamic aircraft performance the overall noise benefit may be quite limited or even completely cancelled. Thus,

noise reduction represents a highly multidisciplinary problem. The DLR project LEISA1 combines and focuses

activities in the research areas of high lift system design, flow control and aeroacoustic design methods, which, up to

now, have been carried out almost independently. The development of a noise estimation tool that enables the

assessment of high-lift devices noise generation already during the design process is one substantial part of the

LEISA project. Based on turbulence and flow field data provided by RANS computations, which are standard for

the aerodynamic performance optimization2, a very fast noise assessment method was developed and experimentally

validated. This method will finally allow for a comparison of different aerodynamic configurations of a high lift

system.

II. Basic Equations for the Noise Estimation Model

In many cases edge noise represents the most relevant high lift systems noise source as e.g. slat noise which is

regarded as being dominated by slat trailing edge noise. The sound pressure generated by a turbulent flow past a

trailing edge can be expressed according to Ffowcs-Williams and Hall3 as (zero sweep of trailing edge)

02/3

0002/1

3

2/1

)]2/sin(2)2/cos()[(sin)2/cos(32

|~| dVrρRπ

kp

V

−−−′ ∫ θθϕθ θθ vvvvr

22

r (1)

Herein the volume integral provides a formulation for the source strength which can be evaluated by making use

of numerically derived flow characteristics. Parameters are the wave number k, the average fluid density ρ, the local

(unsteady) flow velocity components υr and υθ in radial and azimuthal directions of an axis-symmetric coordinate

system aligned with the trailing edge (Fig. 1).

N

American Institute of Aeronautics and Astronautics 092407

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The distance from the observer to the noise source

(coordinate origin) is denoted by R, its azimuthal position

by the angle θ , where θ = 0, 2π are the surfaces of the

plate and ϕ is the polar angle between the direction of the

observer and the trailing edge. The integration variables

are denoted with 0 and dV0 represents the differential

volume element of the integral.

In order to estimate all terms on the basis of available

RANS flow data some assumptions have to be introduced.

The characteristic signal frequency generated by a

turbulence element of size L , convecting past an edge

with a speed proportional to the mean flow speed U is

approximated by LUf /~ , which results in the same

frequency of the radiated sound signal λaf /~ 0 of

wavelength λ , i.e. the wave number may be estimated to

give

.2~2

0La

U

λ

πk π= (2)

The mean local flow velocity U can be determined directly from RANS data, the mean turbulence length scale

can be derived from the turbulence kinetic energy and the dissipation rate is provided by the RANS data according

to

t

t

ω

kL

21

´~ . (3)

The radial and azimuthal velocity components υr and υθ are decomposed into a mean and a fluctuating

component according to

'rrr vvv += and 'θθθ vvv += . (4)

For the evaluation of 2rv the time independent term

2rv can be neglected, because it does not contribute to the

solution. Since 2

rv′ is considered to be significantly smaller than rrvv ′2 it will also be neglected. Hence the velocity

components υr and υθ can be expressed as

rrr vvv ′2~2

and θθθ vvv ′2~2

. (5)

Based on the same assumptions the term υrυθ can be written as

rrr vvvvvv ′+′ θθθ ~. (6)

In case also anisotropy information is available from the flow solution, e.g. when a Reynolds stress turbulence

model is applied, υ'r and υ'θ are estimated by the rms values of the respective velocity fluctuations in radial and

azimuthal directions. Otherwise isotropic turbulence has to be assumed and thus the unsteady part of the radial and

azimuthal velocity are approximated to scale like tr kv3

2~' and tkv3

2~'θ . Finally, in order to estimate the

volume integral from the RANS data of the 2D edge geometry, we need to approximate the dependence of the

Figure 1. Definition of coordinate system at the

trailing edge.

American Institute of Aeronautics and Astronautics 092407

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farfield acoustic pressure from the span b . For a finite span the farfield sound intensity 2'~ p should scale linearly

with span, i.e. bp ~'2 ; on the other hand there has to exist a dependency on the spanwise turbulence length

scale L . For dimensional reasoning the dependency of the source integral along the spanwise direction 0z (as part

of the volume integral) should scale like bL , i.e. ∫∫∫ ∫∫∫∞∞∞

=Ab AV

dAbLzddAdV 0000 ...~...... .

The above mentioned reductions enable the use of Ffowcs-Williams and Hall’s expression in conjunction with

RANS flow field data in order to rank order the noise generation of different trailing edge noise dominated sound

sources. The formulation presented in Eq. (7) below presumes the availability of anisotropy information while

Eq. (8) is based on the assumption of isotropic turbulence (anisotropy in length scales neglected).

( )0

23

0002

1

0)

2sin()()

2cos(sin)

2cos(

2

/~' dArvvvvvvvv

R

abUp

A

rrrr

−

∫∫∞

′+′−′−′ θθϕθρ

πθθθθ

(7)

or for isotropic turbulence

( ) 02

3

0002

1

032

)2

sin()()2

cos(sin)2

cos(2

/~' dArvvvvk

R

abUp

A

rrt

−

∫∫∞

+−−

θθϕθρ

πθθ . (8)

The surface element 0dA is separated into 000 θddrr and will be evaluated numerically. The integral explicitly

takes into account

1) the presence of turbulence in the vicinity of the edge through 0r and

2) the way in which the sound depends on the actual local mean flow field and turbulence distribution. For the

typical assumption 2~ Ukt

(7) would as usual display an explicit velocity to the 5th

power trailing edge law.

III. Numerical and Experimental Validation of Noise Estimation Approach

In order to validate this approach, numerical and experimental

studies on trailing edge noise were conducted. The scope of these

tests was to generate different turbulence levels at the airfoil’s

trailing edge and to (i) examine the noise generation and (ii) to

compare the numerically and experimentally derived mean and

fluctuating velocities at the trailing edge.

A. Set-up of Experimental Studies

Noise and flow measurements were performed on a 2D

NACA0012 airfoil in DLR’s Acoustic Wind Tunnel Braunschweig

AWB (Fig. 2). The airfoil exhibits a chord length of 0.4 m, a wing

span of 0.8 m and is equipped with 46 pressure tabs in order to

determine the static pressure distribution for later comparison with

flow computations and a proper adjustment of the angle of attack of

0° which was kept constant for the wind tunnel tests conducted at

flow speeds of 40 m/s, 50 m/s and 60 m/s. The airfoil’s trailing edge

exhibits a thickness of less than 0.15 mm for minimal bluntness

noise.

Figure 2. Set-up of the NACA0012

airfoil in the Acoustic Wind Tunnel

Braunschweig. View with acoustic mirror

in front.

American Institute of Aeronautics and Astronautics 092407

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NACA0012

10.2 0.4 0.6 0.8

Position of free transition

app. 43 % – 45 %Tripping positions

x/c

NACA0012

10.2 0.4 0.6 0.8

Position of free transition

app. 43 % – 45 %Tripping positions

x/c

Figure 3. Positions of transition fixation at NACA0012 airfoil.

Trailing edge

Wake measurement10 mm downstream

of trailing edge

Hotwire

Trailing edge

Wake measurement10 mm downstream

of trailing edge

Hotwire Figure 4. Positions of hotwire measure-

ments at the trailing edge and in the wake

of the NACA0012 airfoil.

In order to generate different

turbulence levels at the trailing edge

transition tripping was applied. At first the

position of free transition of the boundary

layer was examined by means of a

stethoscope. I turned out that the free

boundary layer transition occurs at about a

43% to 45% chord position. Based on this

finding boundary layer tripping of about

0.15 mm thickness was applied at three

locations upstream of the location of free

transition, i.e. at 20%, 30% and 40% chord

as depicted in Fig. 3.

Noise measurements were performed with an acoustic mirror

of 1.4 m diameter in order to localize noise sources and to

quantify and characterize trailing edge noise for the NACA0012

profile and different tripping configurations, respectively. For that

reason the acoustic mirror (installed on a 3D traversing

mechanism) was traversed along the airfoil chord in a midspan

cross-section. Noise data were digitized with a 125 kHz sampling

rate providing useful data up to 50 kHz. The FFT analysis was

performed with a bandwidth of ∆f = 24 Hz and 2048 averages

were taken in the frequency domain in order to reduce the data

scatter due to low frequency wind tunnel shear layer fluctuations.

In addition velocity data were acquired in the vicinity of the

trailing edge by means of a hotwire sensor, (i) in the wake area of

the airfoil 10 mm downstream of the trailing edge and (ii) directly

at the trailing edge, providing the total mean and fluctuating

velocity for every measurement point (Fig. 4). Both

measurements were performed in perpendicular direction to the

airfoil chord with a single hotwire.

B. Results of Noise Measurements

In a first step noise data were analyzed in order to determine noise source locations. A typical noise source

distribution is depicted in Fig 5. in terms of 1/3-octave band levels for frequencies of 3.15 kHz and 6.3 kHz, for the

model in a configuration with tripping applied at a 20% chord position and flow speeds of 40, 50 and 60 m/s. As

expected a very small level peak occurs at the airfoil’s leading edge, while the major noise source is located at the

trailing edge. This result proves that the noise generation of the NACA0012 airfoil is dominated by trailing edge

noise. The data presented in Fig. 5 also show a systematic trend to higher sound pressure levels with increasing flow

speed. In order to determine the dependency of flow speed on sound pressure levels, the noise data as acquired at the

trailing edge position (x=0 mm) were normalized on a Strouhal number basis assuming an arbitrary reference

dimension of 1 m. Sound pressure levels were normalized according to a 5th

power velocity law (52 ~ Up′ ) taking

Uref=60 m/s as a reference free stream velocity. As depicted in Fig. 6 a reasonable data collapse is achieved by this

normalization again indicating the dominance of trailing edge noise.

American Institute of Aeronautics and Astronautics 092407

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X-Position [mm]

1/3

-octa

ve

Ba

nd

Le

ve

l[d

B]

-500 -400 -300 -200 -100 0 1060

65

70

75

80

85U

inf= 60 m/s - 3.15[kHz]

Uinf

= 50 m/s - 3.15[kHz]U

inf= 40 m/s - 3.15[kHz]

Uinf = 60 m/s - 6.30[kHz]Uinf = 50 m/s - 6.30[kHz]Uinf = 40 m/s - 6.30[kHz]

Angle of attack α = 0 deg

Figure 5. Noise source distribution acquired for

NACA0012 airfoil for 40 m/s, 50 m/s and 60 m/s flow

speed, transition tripping applied at 20% chord

length and a 0° angle of attack.

Sr = 1 m * fm

/ Uinf

Ln

orm

=L

me

as

-5

0*l

og

10(U

/60

m/s

)

100 200 300 400 50075

80

85

90

95

NACA0012 - Tripping 20% - Uinf

=60 m/sNACA0012 - Tripping 20% - U

inf=50 m/s

NACA0012 - Tripping 20% - Uinf

=40 m/s

Figure 6. Effect of flow speed on trailing edge

noise sound pressure level spectra for NACA0012

airfoil with transition tripping applied at 20%

chord length and a 0° angle of attack.

1/3-octave Band Frequency[Hz]

1/3

-octa

ve

Ba

nd

Le

ve

l[d

B]

1000 1000065

70

75

80

NACA0012 - Tripping 20%NACA0012 - Tripping 30%NACA0012 - Tripping 40%

Uinf

=60 m/sAngle of attack α = 0 deg

Trailing edge noiseis dominant

Figure 7. Effect of different tripping positions on

trailing edge noise generation for 60 m/s free stream

velocity and an angle of attack of 0°.

In a next step the influence of different tripping

positions on trailing edge noise was investigated. Prior

to the corresponding noise measurements the

effectiveness of each tripping condition was examined

by means of a stethoscope. It turned out that

downstream of each tripping device a turbulent

boundary layer evolved and consequently the

turbulence levels at the trailing edge of the

NACA0012 airfoil should differ for the test cases

under consideration. Sound pressure level data as

obtained with the acoustic mirror at the position

x=0mm are depicted in Fig. 7 in terms of 1/3-octave

band level spectra. As can be seen the different

turbulent boundary layer conditions at the trailing

edge lead to sound pressure level differences for

frequencies below 2.5 kHz while no change level

change is observed for frequencies above 2.5 kHz.

The sound pressure level spectra show lowest

levels for the most downstream 40% chord tripping

position and a systematic level increase for the more upstream 30% and 20% chord tripping positions. This result

documents the dependency of trailing edge noise levels on local turbulence levels at the trailing edge which in a first

step should be derived from flow computations for a NACA0012 airfoil in order to estimate noise level changes due

to different turbulence levels at its trailing edge.

American Institute of Aeronautics and Astronautics 092407

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Figure 10. Example for computational grid

around NACA0012 airfoil

Mean Local Flow Velocity [m/s]

Ve

rtic

alP

ositio

nw

.r.t

.T

railin

gE

dg

e[m

m]

2530354045505560-100

-50

0

50

100

Tripping@20% chord lengthTripping@30% chord length

Tripping@40% chord lengthTripping@40% chord length - wake measurement

Uinf

=60 m/sAngle of attack α=0 deg

Figure 8. Mean local flow velocities in the wake and

at the trailing edge of the NACA0012 airfoil for

different tripping positions for 60 m/s free stream

velocity and an angle of attack of 0°.

Local Fluctuating Velocity [m/s]

Ve

rtic

alP

ositio

nw

.r.t

.T

railin

gE

dg

e[m

m]

0.5 1 1.5 2 2.5 3-100

-50

0

50

100

Tripping@20% chord length

Tripping@30% chord lengthTripping@40% chord lengthTripping@40% chord length - wake measurement

Uinf

=60 m/sAngle of attack α=0 deg

Figure 9. Local fluctuating velocities in the wake

and at the trailing edge of the NACA0012 airfoil for

different tripping positions for 60 m/s free stream

velocity and an angle of attack of 0°.

C. Results from Hotwire Measurements

Hotwire measurements were conducted to quantify the local flow conditions at the trailing edge of the

NACA0012 airfoil for different transition locations. The acquired mean flow velocities are shown in Fig. 8 and the

corresponding fluctuating velocities are presented in Fig. 9. The results show smallest flow speeds for the most

downstream transition location of 40% chord length and a systematic velocity increase for the more upstream

transition locations of 30% and 20% chord length. In order to compare measured and computed flow properties also

the local flow speed in the wake of the airfoil was determined. As presented in Fig. 8 and Fig. 9 the velocity profile

acquired in the wake area is almost symmetric indicating that a zero degree airfoil angle of attack was accurately

adjusted.

D. Numerical Database for Validation Study

RANS calculations were conducted with DLR’s

flow solver FLOWer4 to determine local flow

properties which should serve as input for the noise

estimation procedure. The RANS mean flow was

calculated on a structured grid consisting of 10 blocks

and a total of 45466 grid points (Fig. 10). Special

emphasis was laid on the grid resolution in the vicinity

of the trailing edge to enable a good representation of

small velocity fluctuations.

In the FLOWer Code different turbulence models

are implemented. These are a two-equation κ−ω

transport model and alternatively a Reynolds stress

turbulence model5. For the present study the κ−ω

shear stress model developed by Menter6 was chosen

as representative two-equation turbulence model.

American Institute of Aeronautics and Astronautics 092407

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Figure 11. RANS computation of the Mach

number distribution around the entire NACA0012

Figure 12. Computed distribution of turbulence

kinetic energy by application of the RSM turbulence

model in the vicinity of the trailing edge of the

NACA0012 airfoil. Transition tripping applied at

20% (top) and 40% (bottom)

Figure 13. Computed distribution of turbulence

kinetic energy by application of the κ−ωκ−ωκ−ωκ−ω-turbulence

model in the vicinity of the trailing edge of the

NACA0012 airfoil. Transition tripping applied at

20% (top) and 40% (bottom) chord length.

RANS calculations were conducted for a Reynolds

number of 1.6*106 based on the model’s 0.4 m chord

length and a free stream velocity of 60 m/s in order to

meet the experimental conditions in the wind tunnel.

Figure 11 shows a typical computed Ma number

distribution for the entire airfoil (top) and in the

vicinity of the trailing edge (bottom). As expected the

flow field around the model is symmetric to the

airfoil’s chord axis for the considered zero degree

angle of attack case. The flow representation in the

vicinity of the trailing edge shows the velocity deficit

in the wake.

Since the production of turbulence kinetic energy

is proportional to the magnitude of fluctuating

velocities, which are input data for the noise

estimation procedure, the distribution of turbulence

kinetic energy in the vicinity of the airfoils’ trailing

edge will be compared for the different turbulence

models which were applied for this study.

The computed distribution of turbulence kinetic

energy by means of the RSM model is depicted in

Figure 12. The upper half of this figure shows the

result for boundary layer transition at 20% chord

while in the lower half the respective data for

transition at 40% chord is displayed. Comparing the

results for both test cases it is obvious that higher

turbulence levels were computed for boundary layer

transition at 20% chord. As presented in Fig. 13 this

finding in principle also holds true for the turbulence

kinetic energy distribution when computed by means

of the κ−ω turbulence model although the difference in turbulence level computed for different transition positions

is not as pronounced as obtained for the computation with the RSM turbulence model. Finally the overall turbulence

levels computed by means of the κ−ω model are about a factor of two smaller than those presented in Fig. 12 for the

computation with the RSM model.

The results obtained so far show a good qualitative agreement between measurement and RANS based

computation in terms of turbulence generation in the vicinity of the trailing edge of the airfoil.

American Institute of Aeronautics and Astronautics 092407

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Vertical Distance to Trailng Edge [mm]

Flu

ctu

atin

gV

elo

city

V' rm

s[m

/s]

0 5 10 15 200

1

2

3

4

5

6

7

8

Transition 20% - measurement

Transition 30% - measurementTransition 40% - measurement

Transition 20% - κ−ω modelTransition 30% - κ−ω modelTransition 40% - κ−ω model

Transition 20% - RSM modelTransition 30% - RSM model

Transition 40% - RSM model

2 mm

Figure 14. Velocity profiles perpendicular to the trailing

edge for computations with the κ−ωκ−ωκ−ωκ−ω-turbulence model and

RSM turbulence model and measurement.

E. Comparison of Fluctuating Velocities in the Vicinity of the Trailing Edge of the NACA0012 Airfoil

Since the fluctuating velocities in the vicinity of a trailing edge govern the respective trailing edge noise

generation and therefore serve also as input for the noise estimation approach a more detailed comparison of the

results obtained both experimentally and numerically is conducted.

Hotwire measurements were conducted by means of a single wire probe. Therefore the total fluctuating velocity

data from the experiment can be compared with the numerical data. Considering the respective results obtained by

means of the κ−ω turbulence model fluctuating velocity data can only be derived from the turbulence kinetic energy.

The dependence of the turbulent kinetic energy from the rms-value of the velocity fluctuations rmsU ′ , which

corresponds to the data that were acquired by means of the hotwire measurements, can be expressed as

2

2

rmst

Uk

′= (9)

Based on the assumption of isotropic turbulence rmsU ′ can be expressed as 2'3u with 'u representing the

velocity fluctuation in one direction. Introducing this in Eq. (9) 2'u can be written as tku3

2'2 = . For the two-

dimensional flow this leads to the expression

trms kU3

4=′ , (10)

for the rms-value of the velocity fluctuations.

In case of the Reynolds stress model the fluctuating velocities are incorporated in the Reynolds stress tensor

which is explicitly calculated. The rms-value of the fluctuating velocity was evaluated by adding up the components

of the velocity fluctuations. Corresponding profiles of fluctuating velocity for all transition positions are plotted in

Fig. 14. The solid lines represent the measurement and show a systematic increase of fluctuations for more upstream

transition locations or increasing boundary layer thickness, respectively. The dash-dotted lines indicate the

computational results obtained by means of the κ−ω turbulence model. Compared to the measured data the

computed effect of different tripping locations on the fluctuating velocity starts at a much larger vertical distance to

the trailing edge. Also the absolute levels are much higher than those obtained with the hotwire. Up to a distance of

about 2 mm to the trailing edge the computed data

also show a systematic trend to higher

fluctuations with increased boundary layer

thickness due to a more upstream transition. The

velocity fluctuation derived from the Reynolds

stress tensor is plotted in Fig. 14 as dashed lines.

As could be expected from the data shown in

Fig. 12 and Fig. 13 the computed velocity

fluctuations based on the RSM model exceed

those computed by means of the κ−ω model.

Again beyond a distance of about 2 mm to the

trailing edge a systematic increase of fluctuations

with increasing boundary layer can be observed.

Both computational results have in common that

for distances to the trailing edge of less than 2

mm no influence of different boundary layer

thicknesses can be observed. The outcome of this

study was, that at least for this simple test case,

the tested turbulence models show in principle the

same characteristics as were obtained for the

American Institute of Aeronautics and Astronautics 092407

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Po

lar

Ra

dia

tio

nA

ng

leΘ

[de

g]

OASPL [dB]

0

3060

90

120

150

180

210

240

270

300

330

7075808590

Transition 20%, RSM modelTransition 30%, RSM modelTransition 40%, RSM model

Figure 15. Computed OASPL for different

transition locations on the NACA0012 using

turbulence data based on the RSM turbulence model.

Po

lar

Ra

dia

tion

An

gle

Θ[d

eg

]

OASPL [dB]

0

30

60

90

120

150

180

210

240

270

300

330

657075808590

Transition 20%, κ−ω modelTransition 30%, κ−ω modelTransition 40%, κ−ω model

Figure 16. Computed OASPL for different

transition locations on the NACA0012 using

turbulence data based on the κ−ωκ−ωκ−ωκ−ω turbulence model.

measured data. Although the absolute levels differ all RANS data computed within this study should be suitable to

serve as input for the noise estimation tool, because the aim of the tool is to reveal differences between different

configurations but not calibrated absolute sound pressure levels.

IV. Noise estimation for the NACA0012 test cases.

In principle the noise estimation based on RANS data can be performed on the RANS grid itself without major

preparatory work. In order to enable an easier integration of local flow properties according to Eq. (7) or Eq. (8) it is

appropriate to set up a circumferential grid around the trailing edge and interpolate the RANS data on this new grid.

The new circumferential grid covers an angular range of 2π with a resolution of one degree in order to match the

resolution of the original RANS grid. Since the noise estimation procedure aims at the investigation of differences in

noise generation between different configurations of either one airfoil or different high lift systems the radial extend

of the grid should at least cover the entire region around the trailing edge where differences in the fluctuating

velocities are obtained by the RANS computations. In case of the NACA0012 airfoil it was shown that meaningful

differences of fluctuating velocities occur for distances of up to 10 mm from the trailing edge. Therefore the grid

size in radial direction was set to 10 mm or 0.025 in a normalized length scale when referenced to the airfoil’s chord

length. The results obtained in terms of overall sound pressure levels for a constant observer distance of 1 m around

the trailing edge of the airfoil are presented in Fig. 15. and Fig. 16. The results depicted in Fig. 15 are based on a

RANS computation using the RSM turbulence model while the data presented in Fig. 16 is based on the

κ−ω turbulence model.

As can be seen both computations result in a systematic sound pressure level increase for more upstream

transition locations corresponding to the higher turbulence levels that occur with increasing boundary layer

thickness due to the enforced transition. The computed level differences of about 0.6 up to 1.1 dB agree reasonably

well to those obtained by the measurements for the corresponding test cases as presented in Fig. 7.

Since the noise estimation procedure should finally be introduced in the high lift system optimization process the

outcome of the noise estimation should be one criterion that could be introduced in a cost function. Based on the

available data the overall sound pressure level for a certain radiation angle may serve as such a criterion. Therefore a

comparison of overall sound pressure levels for a polar radiation angle of 90 degrees is presented in Table 1 for the

measurements as well as for the computational results.

American Institute of Aeronautics and Astronautics 092407

11

Figure 17. Comparison of reference slat system (top)

and low noise slat system (bottom) with Very Long Chord

Slat (VLCS)

As can be seen from the data presented in Table 1 the overall sound pressure levels which have been computed

are about the factor of 1.5 higher than those obtained by the measurements. This fact can be neglected because the

noise estimation approach aims at the identification of differences in noise generation within a number of variants of

one airfoil or high lift system. Regarding the sound pressure level differences that can be obtained from this data it

turns out that both the computed and the measured data exhibit level differences in the order of 0.5 dB. This finding

indicates that the noise estimation procedure leads to reasonable results. Furthermore, at least for this simple test

case, the result achieved by the noise estimation does not depend on the turbulence model used for the RANS

computation.

V. First Application to High Lift Devices

One basic approach within the project LEISA was the design of a low noise 3-element high lift system.

Consequently the new acoustic design tool was applied to these test cases as well. Based on the 3-element reference

configuration a new slat system was designed in order to (i) maintain the aerodynamic performance and (ii) reduce

the slat noise generation.6 To achieve the latter special emphasis was given on the reduction of the local flow

velocity at the slat trailing edge in order to reduce slat trailing edge noise.7 It turned out that an increased slat chord

together with an increased overlap of the device, as depicted in Fig. 17, is able to preserve or even enhance the

aerodynamic performance while at the same time the local flow velocity at the slat trailing edge is slightly reduced.

The respective results are presented in Fig. 18 in terms of static pressure distributions and lift polars for both slat

systems.

Wind tunnel experiments with this new

device called “Very Long Chord Slat” (VLCS)

were conducted to examine both the

aerodynamic performance and the noise

generation. The noise data acquired in AWB by

means of farfield microphones were used to

check the acoustic prediction method. Noise

measurements were conducted at a flow speed

of 60 m/s and the final comparison of noise data

was conducted for equivalent lift for each of the

different high lift systems. This led to an angle

of attack of α=11° for the reference

configuration and α=9° for the VLC slat

configuration.

89.1

89.7

90.4

Estimated OASPL

RSM model

[dB]

74.487.2

Transition @ 40% chord

length

74.888.3Transition @ 30% chord

length

75.289.1Transition @ 20% chord

length

Measured

OASPL

[dB]

Estimated OASPL

SST model

[dB]

NACA0012

Configuration

89.1

89.7

90.4

Estimated OASPL

RSM model

[dB]

74.487.2

Transition @ 40% chord

length

74.888.3Transition @ 30% chord

length

75.289.1Transition @ 20% chord

length

Measured

OASPL

[dB]

Estimated OASPL

SST model

[dB]

NACA0012

Configuration

∆ = 0.7 dB

∆ = 0.6 dB

∆ = 0.8 dB

∆ = 1.1 dB

∆ = 0.5 dB

∆ = 0.4 dB

Table 1. Computed and measured OASPL for the NACA0012 airfoil. Data obtained for a

polar radiation angle of 90 degree and an observer distance of 1 m.

American Institute of Aeronautics and Astronautics 092407

12

Distance to Traling Edge [mm]

Flu

ctu

atin

gV

elo

city

[m/s

]

0 1 2 3 4 5 60

2

4

6

8

3eRef - 11 deg - κ−ω turbulence model

VLCS - 9 deg - κ−ω turbulence model

r = 2 mmdefines size ofintegration area

Figure 19. Velocity profiles perpendicular to the

trailing edge for computations with the κ−ωκ−ωκ−ωκ−ω-

turbulence model for the reference slat system and the

VLC slat system.

Po

lar

Ra

dia

tion

An

gle

Θ[d

eg

]

OASPL [dB]

0

30

60

90

120

150

180

210

240

270

300

330

50556065707580

3eRef - α=11 degVLCS - α=9 deg

Figure 20. Computed OASPL for reference slat

system and VLC slat system. using turbulence

data based on the κ−ωκ−ωκ−ωκ−ω turbulence model

1/3 octave Band Frequency [Hz]

1/3

octa

ve

Ba

nd

Le

ve

l[d

B]

5000 10000 15000 2000065

70

75

80

85

3eRef - Uinf=60 m/s - alpha=11.0 degVLCS - Uinf=60 m/s - alpha=9.0 deg

Figure 21. Measured farfield noise data as obtained for

the reference and the VLC slat system for a free stream

velocity of 60 m/s and a polar radiation angle of 90°.

x [mm]

Cp

0 100 200 300 400 500 600

-7

-6

-5

-4

-3

-2

-1

0

VLCS CLmax

VLCS LDmaxReferenz

NWBgeschlossene KanalwändeMa = 0,13Re = 1,7⋅10

6

α = 10°

F15, M=0.2, Re=12x106

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-10.00 0.00 10.00 20.00 30.00 40.00αααα

C L

reference

VLCS-CL,max

VLCS-L/Dmax

Figure 18. Static pressure distributions and lift polars acquired for the reference slat system and

the VLC slat system.

A. Noise Estimation Results.

In order to determine the size of the integration

area needed for the noise estimation the distribution

of fluctuating velocities in the vicinity of the slat

trailing edge was determined. Since the RANS

computation was performed with the κ−ω turbulence

model the fluctuating velocity distribution was

derived from the distribution of turbulence kinetic

energy. As depicted in Fig. 19 the most significant

differences of the fluctuating velocities arise up to a

distance of about 2 mm to the trailing edge.

Consequently the integration was performed on a

circumferential grid with radius r=2 mm as indicated

in Fig. 19.

The final result of the noise estimation is

depicted in Fig. 20. By means of the computation a

noise level reduction of up to 2 dB is estimated for

the VLCS configuration compared to the reference

slat system.

American Institute of Aeronautics and Astronautics 092407

13

84.474.2

VLCS high lift system

89.276.03 element reference system

Measured

OASPL

[dB]

Estimated

OASPL

[dB]

F16

Configuration

84.474.2

VLCS high lift system

89.276.03 element reference system

Measured

OASPL

[dB]

Estimated

OASPL

[dB]

F16

Configuration

∆ = 1.8 dB ∆ = 4.8 dB

Table 2. Comparison of computed and measured

OASPL for reference slat system and VLC slat system.

This finding compares reasonably well to the outcome of the measurements in AWB presented in Fig.22 in terms

of 1/3-octave band level spectra. The spectra show a broadband noise level reduction of up to 5 dB for the VLC slat

compared to the reference slat. In order to provide a single criterion to be used in an high lift systm optimization

process the measured and computed overall sound pressure levels were derived from the respective data and listed in

Table 2. The computed overall sound pressure levels exhibit a noise reduction of 4 dB for the VLCS configuration

compared to a 5 dB noise reduction determined from the measured data. As can be seen the noise reduction provided

by the VLC slat system can be predicted with this method.

VI. Conclusion

Within the mainframe of the DLR project LEISA a first approach towards a fast noise estimation tool could be

established. This in fact represents a postprocessing tool of the RANS data and enables a fast comparison of the

noise generation of different 3 element high lift systems based on flow characteristics provided by RANS based flow

solvers. As shown for the trailing edge case this tool may provide reasonable trend information within a design

process. Therefore this method may serve as an engineering tool within the aerodynamic optimization process of

high lift systems.

References 1 Wild, J. Pott-Pollenske, M. Nagel, B.: ”An Integrated Design Approach for Low Noise Exposing High-Lift Devices”,

AIAA-2006-2843, 3rd AIAA Flow Control Conference, San Francisco, CA, USA, 5-8 June 2006 2 Wild, J.: “Validation of Numerical Optimization of High-Lift Multi-Element Airfoils based on Navier-Stokes-Equations”,

AIAA Paper 2002-2939, 20th AIAA Applied Aerodynamics Conference, June 24-26, 2002, St. Louis, Missouri, USA 3 Ffowcs-Williams, J.E., Hall, L.H.: “Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half

plane”. Journal of Fluid Mechanics, 1970, Vol 40, pp. 657-670. 4 Aumann, P., Bartelheimer, W., Bleecke, H., Kuntz, M., Lieser, J., Eisfeld, B., Fassbender, J., Heinrich, R., Kroll, N.,

Mauss, M., Raddatz, J., Reisch, U., Roll, B., Schwarz, T.: „FLOWer Installation and User Handbook“, Braunschweig, Germany,

2000 5 Eisfeld, B., Brodersen, O.: ”Advanced Turbulence Modelling and Shear Stress Analysis for the DLR F6 Configuration”,

AIAA-2005-4727, 23rd AIAA Applied Aerodynamics Conference, Toronto, Canada, June 2005 6 Menter, F. R., "Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications," AIAA Journal, Vol. 32,

No. 8, August 1994, pp. 1598-1605. 7 Pott-Pollenske, M., Alvares-Gonzales, J., Dobrzynski, W.: ”Effect of Slat Gap on Farfield Radiated Noise and Correlation

with Local Flow Characteristics”, AIAA-2003-3228, 9th AIAA/CEAS Aeroacoustics Conference, 12-14 May 2003, Hilton Head,

South Carolina, USA